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        <td class="header">&nbsp; Dual-pol Radar Vegetation Index Generation</td>
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<h3>Dual-pol Radar Vegetation Index-DpRVI</h3>
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<p align="right"><a href="http://www.mrslab.in" target="blank"><img src="images/MRSLABlogo.png"></a></p>
<p align="right">Microwave Remote Sensing Lab (MRSLab)</br>
Indian Institute of Technology Bombay, India</br>
Contributors: Dr. Dipankar Mandal</br>
Tel: +91-22-2576-7677</br>
Date: 25 Nov 2020</br>
E-mail: mrscsre@gmail.com; dipankar.agrilengg@gmail.com</br>
URL: http://www.mrslab.in
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<h3>1. DpRVI Theoretical Introduction </h3>
<p>The Dual-pol Radar Vegetation Index (DpRVI) is calculated from dual-pol 2x2 covariance matric C2.</p>
<p align="center"><img src="images/c2matrix.PNG"></p>
<p>The scattering information in
terms of the degree of polarization and the eigenvalue spectrum are jointly utilized to
derive the vegetation index from dual-pol SAR data. The state of
polarization of an EM wave is characterized in terms of the degree of
polarization (m) as proposed by Barakat (1977):</p>
<p align="center"><img src="images/dop.PNG"></p>
<p>where Tr is the matrix trace operator (i.e., the sum of the diagonal
elements) and |.| is the determinant of a matrix.</p>

<p>The two non-negative eigenvalues (lambda1>=lambda2>=0) are obtained from the eigen-decomposition of the C2 matrix which are then normalized with the total power Span (Tr(C2) = lambda1 + lambda2).
The eigenvalues quantify the dominancy of scattering mechanisms. Hence, the parameter beta is introduces as beta = lambda1/Span</p>
<p>The dominant scattering information is modulated with the degree
of polarization (m), which in particular characterizes anisotropy for
dual-pol SAR data. The scattering randomness is then obtained by
subtracting m x beta from unity, as given in the following equation by Mandal et al. (2020).</p>
<p align="center"><img src="images/dprvieq.PNG"></p>

<p>Ref:</br>
[1] Barakat, R., 1977. Degree of polarization and the principal idempotents of the coherency
matrix. Opt. Commun. 23 (2), 147-150.</br>
[2] D. Mandal, V. Kumar, D. Ratha, S. Dey, A. Bhattacharya, J. M. Lopez-Sanchez, H. McNairn, Y. S. Rao, "Dual Polarimetric Radar Vegetation Index for Crop Growth Monitoring Using Sentinel-1 SAR Data," Remote Sensing of Environment, 247: 111954, 2020, DOI:10.1016/j.rse.2020.111954.</p>

<h3>2. DpRVI Algorithm Specification </h3>
<p>The general workflow to generate DpRVI from Sentinel-1 SLC products is highlighted in the following figure.</p>
<p align="center"><img src="images/processingflow.png" style="height:150%"></p>
<p align="center">Sentinel-1 preprocessing workflow for time-series data to generate DpRVI.</p><br>
<p> The preprocessing workflow (Graph .xml file) can be found in https://github.com/mrslab-iitb/sentinel-1-SLC-preprocessing-polarimetry. ; 
</br> Read more about Graph processing Sentinel-1 C2 matrix at:</br> 
[Ref] : Mandal, D.; Vaka, D.S.; Bhogapurapu, N.R.; Vanama, V.S.K.; Kumar, V.; Rao, Y.S.; Bhattacharya, A. Sentinel-1 SLC Preprocessing Workflow for Polarimetric Applications: A Generic Practice for Generating Dual-pol Covariance Matrix Elements in SNAP S-1 Toolbox. Preprints 2019, 2019110393 (doi: 10.20944/preprints201911.0393.v1).</p>


<h3>3. DpRVI Processor Documentation </h3>
<p>Inputs to DpRVI processor:</br>
C2 matrix of Sentinel-1 like dual-pol data.-->data type: float32</br>
Processing window size--> data type int</p>

<p>Output of DpRVI processor:</br>
dprvi image-->data type: float32</p>
<p align="center"><img src="images/toolinterface.png" style="height:70%"></p>




<h3>4. DpRVI Results Analysis Help </h3>
<p>For results analysis please follow the article "D. Mandal, V. Kumar, D. Ratha, S. Dey, A. Bhattacharya, J. M. Lopez-Sanchez, H. McNairn, Y. S. Rao, "Dual Polarimetric Radar Vegetation Index for Crop Growth Monitoring Using Sentinel-1 SAR Data," Remote Sensing of Environment, 247: 111954, 2020, DOI:10.1016/j.rse.2020.111954."</p>
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